Dodecakis hecatonicosachoron

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Dodecakis hecatonicosachoron
Rank4
TypeUniform dual
Notation
Coxeter diagramo5o3m3m ()
Elements
Cells1440 pentagonal pyramids
Faces3600 isosceles triangles, 720 pentagons
Edges1200+2400
Vertices120+600
Vertex figure120 dodecahedra, 600 triakis tetrahedra
Measures (edge length 1)
Central density1
Related polytopes
DualTruncated hexacosichoron
Abstract & topological properties
Flag count57600
Euler characteristic0
OrientableYes
Properties
SymmetryH4, order 14400
ConvexYes
NatureTame

The dodecakis hecatonicosachoron, also known as the pentagonal-pyramidal chilliatetracositetracontachoron, is a convex isochoric polychoron with 1440 pentagonal pyramids as cells. It can be constructed as the dual of the truncated hexacosichoron.

It can also be obtained as the convex hull of a hecatonicosachoron and a hexacosichoron, where the edges of the hexacosichoron are times the length of those of the hecatonicosachoron. Varying the hexacosichoron's edge length to be anything less than times that of the hecatonicosachoron gives a fully symmetric variant of this polychoron.